It depends, are you thinking of changing the motherboard because the old one is faulty or do you want an upgrade? If you want to replace because the old one is broken then yes, you do need to get a very similar motherboard.
You'll need an ATX motherboard which has socket 478, able to use 400/533 mhz RAM. If you put "Socket 478" into the search field of ebay, it should give you a few boards there for sale. The model numbers can then be googled to find the exact specifications.

If you are replacing the motherboard for an upgrade, then I personally wouldn't as you may not see much improvement, unless you specifically wanted one with more USB ports or better integrated graphics/sound

You do understand that replacing the board will most likely require at least a repair install of the os correct?
Socket 478 boards are getting pretty hard to find now since the technology is pretty old. Newegg has a few however they are low end via boards; not what I recommend for an intel build.

Tough assignment. Socket 478 boards are no longer made and hard to find. Unless you can get the same make/model, you will likely have to reinstall your windows, reload all your applications, and copy your email folder, browser links, and stored passwords.

If you buy a current processor and CPU, you're looking at around $200US more for something lower end, but your case may not have enough power. and you still have to reinstall everything.